WO 2010/128845 discloses a control unit for a LED assembly and a lighting system. A buck converter supplies a power supply current to a series arrangement of LED's. The LED's can be dimmed by switching on and off the buck converter with a particular power supply duty-cycle. Such a power supply duty-cycle dimming (also referred to as PWM control) is applied to all the LED's in the string and thus does not allow to dim the LED's individually. Alternatively, across each one of the LED's an associated LED switch is arranged. Now, the on and off times of the LED switches can be different for different LED's. When the LED switch is open, the current flows through the LED and when the LED switch is closed the current flows through the LED switch. The LED will be dimmed more if the LED switch closes during a longer percentage of the time. The LED switches are controlled by a microprocessor via associated level converters. In an embodiment, the dimming of the LED's is obtained by a combination of duty-cycle dimming of the LED switches and reducing the power supply current. In this approach, the power supply current supplied by the buck converter is stabilized on different levels such that together with the duty-cycle dimming of the LED switches more intensity steps can be generated.